5.Regarding the equations below. What is the value of x?

5x + 2y = 4
x – 3y = –23

x=−2

y=7

Step-by-step explanation:

5x+2y=4

x−3y=−23

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

5x+2y=4,x−3y=−23

To make 5x and x equal, multiply all terms on each side of the first equation by 1 and all terms on each side of the second by 5.

5x+2y=4,5x+5(−3)y=5(−23)

Simplify.

5x+2y=4,5x−15y=−115

Subtract 5x−15y=−115 from 5x+2y=4 by subtracting like terms on each side of the equal sign.

5x−5x+2y+15y=4+115

Add 5x to −5x. Terms 5x and −5x cancel out, leaving an equation with only one variable that can be solved.

2y+15y=4+115

Add 2y to 15y.

17y=4+115

Add 4 to 115.

17y=119

Divide both sides by 17.

y=7

Substitute 7 for y in x−3y=−23. Because the resulting equation contains only one variable, you can solve for x directly.

x−3×7=−23

Multiply −3 times 7.

x−21=−23

Add 21 to both sides of the equation.

x=−2

The system is now solved.

x=−2,y=7

Graph if needed:

3

step-by-step explanation:

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages